 We're going to do one more example of finding all complex zeros of a polynomial. So this is the second example on your sheet. What we first want to do is look at the graph just like we did before in order to find any real zeros. Remember, while you look at the graph to look for the multiplicity of the zero based on how it hits the x-axis. So this one, since it has a fourth degree, it's a fourth degree polynomial, at the most it will have four distinct zeros. So we'll fill in our blanks with four. So I want you just to pause the video a second and look on your graph to find any zeros of the polynomial. On my graph I found zeros at negative three and one and both of those zeros were just single roots because it went straight through on the graph. So if I have a zero at negative three that means my factor is at x plus three and a zero at one gives me a factor at x minus one. So what I'm going to do is because these two zeros did not appear on the graph that must mean that they are imaginary zeros. And so I'm going to use division in order to reduce the original equation and find the remaining zeros. So I'm going to use synthetic division and I'll first divide by x plus three. So I'll place all of my coefficients in order and then complete the division. Remember to always multiply by the number in the box and then add when you go down. And one good way to always check your work here is the remainder should always be equal zero equal to zero because you're dividing by a factor. So that means it should fit in perfectly. Now with what I have left I'm going to divide by my second factor x minus one and I will just complete that addition here or that division. And what I have left here is one zero twenty five. What that stands for is the equation x squared plus zero x plus twenty five. And since I'm trying to find zeros of a polynomial what I'm going to do to finish this problem is set this final equation equal to zero. And I can solve that in any way I want since it's a quadratic there are lots of options. But here I think the best way to solve that the easiest to me is just to get the x squared by itself and then take the square root of each side. So the square root of negative twenty five is a positive or negative five i. And so my last two zeros are a positive five i and a negative five i. If you don't want to do that one by hand you also could use the quadratic formula by hand or you could use the program on your calculator.